Journal of Thermodynamics

Volume 2015, Article ID 208486, 11 pages

http://dx.doi.org/10.1155/2015/208486

## Scaling Model of Low-Temperature Transport Properties for Molecular and Ionic Liquids

Department of Physics and Materials Science, Odessa National Academy of Food Technologies, Kanatnaya Street 112, Odessa 65039, Ukraine

Received 23 September 2015; Accepted 10 November 2015

Academic Editor: Mohammad Al-Nimr

Copyright © 2015 Vitaly B. Rogankov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The universal scaling concept is applied to the low-temperature range of* any liquid states and substances* located between the melting () and normal boiling () points far away from the critical region. The physical reason to develop such approach is the revealed collapse of all low-temperature isotherms onto the* single universal one* argued by the model of fluctuational thermodynamics (FT) proposed recently by author. The pressure reduced by the molecular parameters of the effective* short-range Lennard-Jones* (LJ)* potential* depends here only on the reduced density. To demonstrate the extraordinary predictive abilities of the developed low-temperature scaling model it has been applied to the prediction of equilibrium and transport (kinetic and dynamic viscosity, self-diffusion, and thermal conductivity) properties not only for* molecular liquids* but also for molten organic salts termed* ionic liquids* (ILs). The best argument in favor of the proposed methodology is the appropriate consistency with the scarce experiments prediction of transport coefficients for ILs on the base of universal scaling function constructed for the* simplest LJ-like liquid argon*. The only input data of any substance for prediction are the linear approximations of -dependent density and isobaric heat capacity taken from the standard measurements at atmospheric pressure.

#### 1. Introduction

The concept of scaling description at low temperatures based on the chosen effective form of a pair interparticle potential is not completely novel. In particular, Hoover et al. [1] used the oversimplified (even in this specific region of a liquid state) so-called* soft-sphere* (ss) purely repulsive functionwith constant ss-parameters and exponent ranging from about six for metals to about twelve for rare gases . Its limitative value for a primitive hard-sphere (hs) model leads the* scaling variable * introduced by the above authors ,to be only -dependent. Another notable feature here is the implied PCS (principle of corresponding states) nature of such ss-scaling. Indeed one has to fix the exponent in (1) and (2) to select the group of similar substances.

Nevertheless the useful consequence of scaling transformation has been noticed by Hoover et al. [1] because any equilibrium or transport reduced properties (e.g., dynamic viscosity or self-diffusion , mass of particle) of different ss-systems with fixed exponent should coincide at the different and being expressed in terms of -variable from (2). Of course, the additional serious restriction of ss-model (common with hs-model) is an absence of gas- (vapor-) liquid transition at any value of repulsive exponent.

It was shown recently [2, 3] in the framework of FT-model [4–6] that the aforementioned oversimplifications of ss- and/or hs-model are not necessary if one considers the more realistic LJ-type potential with the effective -dependent parameters :The advantage of such approach in comparison with the conventional estimates of their constant LJ-counterparts , (mainly, from the experimental second-virial-coefficient’s data) follows from the exact -dependence derived by FT-model for any subcritical temperature:where , , , and is the -dependent parameter of excluded volume.

The determination of both is not trivial task for ILs [7] in which the vapor-pressure curve is inaccessible by the standard lab. vacuum (~10^{−3}, Pa) experiment. However, just this restriction leads to the significant simplification of (4) at low temperatures as is shown in Figure 1 for the well-studied simple and complex substances.